A 3-cup bottle of dish soap costs $5.28. What is the price per fluid ounce?

The properties needed to prove n + n + n + 2n = 5n are: Distributive Property of Multiplication, Associative Property of Addition, and Commutative Property of Addition.

The commutative property of addition states that when two or more numbers are added, the order in which they are added does not affect the sum. In other words, for any two numbers a and b, a + b = b + a.

The properties required to prove n + n + n + 2n = 5n are as follows:

Thus, these properties can be used.

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Final answer:

To prove n + n + n + 2n = 5n, we use the commutative and associative properties of addition to group and combine like terms, then apply the distributive property to show that the sum equals 5n.

Explanation:

To prove the equation n + n + n + 2n = 5n, we need to use properties of equality and algebraic manipulation. First, we apply the commutative property of addition, which allows us to rearrange the terms in any order without changing the sum.

This property isn't strictly necessary here, as all terms involve 'n', but it's a useful property in general for manipulating equations.

Next, we utilize the associative property of addition, which allows us to group numbers in any combination when adding. In this specific case, we group all the 'n' terms together:

(n + n + n) + 2n

Using the associative property, we can simplify the equation further by combining like terms:

3n + 2n = 5n

Lastly, we apply the distributive property, which in this case shows that multiplying the coefficient (being 1 for n in this example) by the number of times 'n' appears (3 for the first set and 2 for the second set), gives the same result as adding 'n' that many times.

Final answer:

Sally paid a $12.50 entry fee to the fair. Joe can buy 18 tickets after paying the entry fee with his $26. The equation to represent the total cost of entry fee and tickets based on the number of tickets purchased is y = 12.50 + 0.75x.

Explanation:

(a) We are told Sally spent a total of $31.25 on the entry fee plus 25 ride tickets. Since each ticket costs $0.75, we can multiply 25 tickets by $0.75 to find the total cost of the tickets alone. That is 25 tickets × $0.75 per ticket = $18.75. Subtracting this amount from the total cost of $31.25 gives us the entry fee. The entry fee is $31.25 - $18.75 = $12.50.

(b) Joe has $26 to spend on the entry fee and tickets. We found out earlier that the entry fee is $12.50. Subtracting the entry fee from the total amount Joe has, we get $26 - $12.50 = $13.50. Now, divide this by the cost of one ticket, $0.75, to determine the number of tickets he can buy: $13.50 / $0.75 = 18 tickets.

(c) Let x represent the number of ride tickets purchased and y represent the total cost of fair entry fee and ride tickets. The total cost is the sum of the fixed entry fee and the variable cost of x tickets at $0.75 each. The equation is y = 12.50 + 0.75x.

The length of each side of the square room with an area 225 ft² is 15 ft.

The area of a square is a product of it's any two sides or a product of diagonals divided by two. If side has a length a then diagonal is a√2.

The perimeter of a square is the sum of the lengths of all the sides.

Given, The area of a square room is 225 ft².

Assuming the length of each side is 'a' feet.

∴ The area of the square room is,

a×a =  225 ft².

a² = 225 ft².

a = ± 15 ft.

As length can not be negative +15 ft is the admissible value.

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Answer:

Here are the options to the questions:  

a.) g(x)=|2(x−5)|

b.) g(x)=|2(x+5)|

c.) g(x)=|2x+5|

d.) g(x)=|2x−5|

The answer is b.) g(x)=|2(x+5)|

Step-by-step explanation:

The function F(x) = |2x| has the vertex at point (0,0)

The rule of translation is (x,y) -------- (x - 5, y)

The translation of the point (0,0)is equal to

(x,y) -------- (0 - 5,0)

(x,y) -------- (-5,0)

The function g(x) has the vertex at point (-5,0)

So therefore, the function g(x) is equal to g(x)=|2(x+5)|

There are two complex roots of the polynomial equation.

They are mathematical expressions involving variables raised with nonnegative integers and coefficients and constants with only operations of addition, subtraction, multiplication, and nonnegative exponentiation of variables involved.

We have been given a polynomial expression as;

[tex]-3x^ 4-7x+17=0[/tex]

Since the Degree of a polynomial is the highest power that its terms (for multi-variables, the power of the term is the addition of the power of variables in that term).

Therefore, the highest power of the given polynomial is 4.

Thus, the Maximum possible roots are 4 but; only 2 are real and 2 are complex.  

Hence, There are two complex roots of the polynomial equation.

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add all the numbers and then divide by how many there are in the set to find the mean so

-11+22+-2+-3=6

6÷4=1.5

so 1.5 would be the mean

Hope this helps!

Answer:To simplify the following expression, we first simplify the terms inside the parenthesis from inner going outer. The first one is [p - (m + n - p)] equal to p - m- n + p = 2p - m - n. Then, n +2p - m - n equal to 2p -m. Then, m -  2p + m equal to 2m -2p. Answer is B

Step-by-step explanation:

The area of the square is the square of the side thus the approximate length of the square will be 21 ft so option (B) will be correct.

A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.

Area of square = Side²

As per the given question,

The area of a square boxing ring is 436 square feet.

It is known that,  

Area = Side²

Side² = 436

Take square root on both sides,

Side = √436 = 20.88 ≈ 21 ft

Hence "The area of the square is the square of the side thus the approximate length of the square will be 21 ft so option (B) will be correct".

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Answer:

The correct answer is 5

Step-by-step explanation:

Compound interest formula is :

[tex]A=p(1+\frac{r}{n} )^{nt}[/tex]

1.

A = 3634.51

p = 2564.65

r = ?

n = 2

t = 13

Putting the values in formula, we get

[tex]3634.51=2564.65(1+\frac{r}{2} )^{2*13}[/tex]

=> [tex]3634.51=2564.65(1+\frac{r}{2} )^{26}[/tex]

=> [tex]\frac{3634.51}{2564.65}=(\frac{2+r}{2} )^{26}[/tex]

=> [tex]1.417=(\frac{2+r}{2} )^{26}[/tex]

We get [tex]\sqrt[26]{1.417}=\frac{2+r}{2}[/tex]

We get r = 0.02699 and r = -4.02699 (neglecting the negative value)

We get r = 0.027 (rounded)

And in percentage, it is 2.7%.

So, option C is the answer.

2.

p = 2651.43

r = 2.8% or 0.028

n = 2

t = 18

Putting the values in formula we get;

[tex]A=2651.43(1+\frac{0.028}{2} )^{2*18}[/tex]

=> [tex]A=2651.43(1.014)^{36}[/tex]

A = $4373.67

So, interest earned = [tex]4373.67-2651.43=1722.24[/tex] dollars

Hence, option D. $1,722.25 is the answer.

To find the percent of increase in the number of drive-in theaters from 1933 to 1945, subtract the initial number from the final number, divide by the initial number, and multiply by 100, resulting in a 2100% increase.

The question asks how to calculate the percent of increase in the number of drive-in theaters in the U.S. from 1933 to 1945. To find the percent of increase you subtract the original number from the new number divide by the original number, and then multiply by 100 to convert to a percentage.

Therefore, the percent of increase from 1933 to 1945 was 2100%.

Answer:

The equation of the line would be y = 6x + 2

Step-by-step explanation:

Since we have a slope (6) and a point (0,2) we can use them in point slope form. The slope goes in for m and the point goes in for (x1, y1).

y - y1 = m(x - x1)

y - 2 = 6(x - 0)

y - 2 = 6x

y = 6x + 2

The expression 36 + 4 can be written as a product using the greatest common factor and the distributive law is 4(9 + 1).

There are three basic math properties they are commutative property which states a + b = b + a, associative property which states

a + (b + c) = (a + b) + c and distributive property which states a(b+c) = ab + ac.

We know distributive property states a(b + c) = ab + ac.

Given 36 + 4, the here greatest common factor of 36 and 4 is 4.

∴ The expression 36 + 4 can be written as,

4(9 + 1).

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Since the problem is requiring us to use the loan repayment calculator and here is what the calculator gave:

Loan Balance: $25,506.00

Adjusted Loan Balance: $25,506.00

Loan Interest Rate: 6.80%

Loan Fees: 0.00%

Loan Term: 10 years

Minimum Payment: $0.00

Monthly Loan Payment: $293.52

Number of Payments: 120 months

Cumulative Payments: $35,223.07

Total Interest Paid: $9,717.07

It is projected that you will need an annual salary of a minimum $35,222.40 to be capable to have enough money to repay this loan. This approximation assumes that 10% of your gross monthly income will be keen to repaying your student loans. This resembles to a debt-to-income ratio of 0.7. If you use 15% of your gross monthly income to repay the loan, you will need an annual salary of only $23,481.60, but you may experience some financial difficulty. This corresponds to a debt-to-income ratio of 1.1.

Answer:

X=4

Step-by-step explanation:

3 * 4 = 12 + 2 = 14.That means your answer is C) 4.

Hope this helps!  :')

To solve this we use the z statistic. The formula for z score is:

z = (x – u) / s

where x is the sample value = less than 16, u is the sample mean = 16.1, s is standard dev = 0.1

z = (16 – 16.1) / 0.1

z = - 1

From the standard distribution tables at z = - 1,

P (z = -1) = 0.1587

So about 15.87% is underweight.

To find the percentage of bags that will likely be underweight (less than 16 ounces), we need to find the area under the normal distribution curve to the left of 16 ounces. The probability is approximately 15.87%.

To find the percentage of bags that will likely be underweight (less than 16 ounces), we need to find the area under the normal distribution curve to the left of 16 ounces. We can use a Z-table or a calculator to find this probability. First, we need to standardize the value of 16 ounces using the formula Z = (X - μ) / σ, where X is the given value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get Z = (16 - 16.1) / 0.1 = -1. This means that 16 ounces is 1 standard deviation below the mean.

Next, we can use the Z-table or a calculator to find the probability associated with a Z-score of -1. From the table or calculator, we find that the probability is approximately 0.1587 or 15.87%. Therefore, approximately 15.87% of the bags will likely be underweight (less than 16 ounces).

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The answer is (x+5)(x-8)